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A firm manufactures three different types of hand calculators and classifies them as small, medium, and large according to their calculating capabilities. The three types hone production requirements given by the following table





Small medium large





Electronic circuit component 5 7 10





Assembly time (n) 1 3 4





Cases 1 1 1





The firm has methyl limit of 90.000 circuit components, 30.000 hours of labor and 9000 cases. If the profit is birr 6 for the small, birr 13 for the medium and birr 20 for the large calculator, then





A. How many of each should be produced to yield maximum profit





B. What is the maximum profit?

Mention 5 elements to cater for the needs of inclusive and non-inclusive learners in a classroom

if 3.00 grams of H2 were produced, how many grams of Al reacted?


Design a circuit that generates 9's compliment of a BCD digit. Optimize your functions, taking advantage of don't care conditions where necessary, and implement using only 2-input NOR gates.


For the function: F(W,X,Y,Z) = "\\prod" M(0,3,4,6,7,9,11,15):

a) identify the essential prime implicants

b) Write the minimal sum


with the aid of an example, explain how even and odd parity work and give an example application where they may be useful.




1. Calculate the pH of the original buffer solution of dihydrogen phosphate/hydrogen phosphate.






2. Calculate the pH The 20 mL (dihydrogen phosphate/hydrogen phosphate buffer) solution when 1 mL of 0.1 molL-1 NaOH has been added






3. Calculate the pH of the 20 mL (dihydrogen phosphate/hydrogen phosphate buffer) solution when 1 mL of 0.1 molL-1 HCl has been added






- Using the Henderson formula for the pH of a solution: pH = pKa + log ([A-]/ [HA]), and show working out







Explain and illustrate why a NAND gate is considered a universal gate


implement a two-level OR-AND logic circuit given the truth table of 3 inputs below:


A B C F

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 0


Given that F(X,Y,Z) = "\\bar{X}" + Z(X+"\\bar{Y}" ) use algebraic manipulation to derive the canonical POS expression for F


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